Twin paradox

This outcome is predicted by special relativity ("time dilation of moving clocks") and can also be verified experimentally, for example with muons produced in the upper atmosphere being detectable on the ground. Without time dilation, the muons would decay long before reaching the ground.

The paradox arises if one takes the position of the travelling twin: from his perspective, his brother on Earth is moving away quickly, and eventually comes close again. So the traveller can regard his brother on Earth to be a "moving clock" which should experience time dilation. Special relativity says that all observers are equivalent, and no particular frame of reference is privileged. Hence, the travelling twin, upon return to Earth, would expect to find his brother to be younger than himself, contrary to that brother's expectations. Which twin is correct?

It turns out that the travelling twin's expectation is mistaken: special relativity does not say that all observers are equivalent, only that all observers in inertial frames are equivalent, i.e. observers which don't undergo acceleration. But the travelling twin most certainly accelerated at least once during his journey and his is therefore not an inertial frame. The twin on Earth rests in an inertial frame for the whole duration of the flight (if we ignore the comparatively small acceleration resulting from Earth's mass and movement) and he is therefore able to distinguish himself from the travelling twin.

It is during the U-turn when, from the point of view of the traveling twin, the twin at rest ages very quickly. This is a purely artificial effect caused by the change in the definition of simultaneity when changing frames. Here's why.

In special relativity there is no concept of absolute present. A present is defined as a set of events that are simultaneous from the point of view of a given observer. The notion of simultaneity depends on the frame of reference, so switching between frames requires an adjustment in the notion of the present. If one imagines a present as a (three-dimensional) plane in Minkowski space, switching frames results in changing the inclination of the plane. The tilting plane of the U-turning twin quickly sweeps the lifeline of the resting twin. Suddenly the resting twin gains years of calculated age in the reckonings of the traveling twin. Note that this has nothing to do with the observed age. Since the twins are separated by a large distance, they can only observe images from the past, not from "the present."

In resolving the paradox, it is sometimes claimed that special relativity cannot be applied to accelerating bodies, and that general relativity has to be used, but this is not correct. For instance, the age of both the Earthbound and travelling twin can be correctly calculated by integrating the spacetime interval (or proper time) over the spacetime paths they make in any inertial frame (these paths are known as the twin's worldlines). Similar methods can be used to calculate the relativistic behaviour of an accelerating spacecraft (see relativistic rocket). SR only becomes inapplicable when the effect of gravity is non-negligible, in which case general relativity must be used.

External references

Referenced By